13)given triangle xyz as shown at right find yz rounded to the nearest tenth

Part 3) Given triangle XYZ as shown at right find YZ rounded to the nearest tenth

we know that
the sum of the internal angles of a triangle add up to 180 degrees
so
m∠X=180-[55+29]----> 96°
applying the law of sines
YZ/sin X=35/sin 55°------> YZ=35*sin 96/sin 55-----> YZ=42.49
YZ=42.5 units

the answer Part 3) is
YZ=42.5 units

Part 4)
we know that
OQ/NQ=PR/NR
NQ=4X+(2X+2)---> 6X+2
OQ=2X+2
PR=15
NR=24+15----> 39
(2X+2)/(6X+2)=15/39
39*(2X+2)=15*(6X+2)
78X+78=90X+30
90X-78X=78-30
12X=48
X=4

The answer part 4) is
x=4

Part 5) A trapezoid  is show below. Calculate the measure of angle x. Round to the nearest tenth of a degree

see the picture with letters attached to better understand the problem

we know that
BC=36-28-----> 8 ft

sin x=BC/AC-----> sin x=8/12
x=arc sin(8/12)-------> x=41.81°------> x=41.8°

the answer Part 5) is
x=41.8°

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